The Excluded Minors for GF(4)-Representable Matroids

The definitions of these matroids, with a summary of their interesting properties, can be found in the Appendix. Except for P"8 , they were all known to be excluded minors for GF(4)-representability (see Oxley [15, 17]). The matroid P"8 is obtained by relaxing the unique pair of disjoint circuit-hyperplanes of P8 . Ever since Whitney's introductory paper [28] on matroid theory, researchers have sought ways to distinguish the representable matroids. For any field F, the class of F-representable matroids is closed under taking minors. Thus, it is natural to characterize the minor-minimal matroids that are not F-representable; we refer to such matroids as excluded minors. Tutte [27] showed that U2, 4 is the only excluded minor for the class of binary matroids. Tutte also showed that the excluded minors for the class doi:10.1006 jctb.2000.1963, available online at http: www.idealibrary.com on